Question
I live in St George, utah -high desert  lawn established, much bermuda grass  have recently developed brown spot that seems to be growing  

Answer
Hi Lew;
Have you had all the " more than normal" rains the rest of us have had?
Could be brown spot fungus.
Damp, cool weather makes perfect conditions for molds and fungus..
Horticultural Corn Meal is an excellent fungicide for large areas. For shrubs and trees that are sunject to black spot fungus and powdery mildew, baking soda disolved in water and sprayed on the whole plant, underneath as well as on top of leaves.
For Horticultural Corn Meal, apply about 10 pounds per 1000 sq.ft.
For black spot on roses etc, put about 1 cup horticultural corn meal per 5 gallons of water, let it set for about 30 minutes or so, strain and put in a sprayer to spray to plants.
It is also good for toenail fungus and athlete's foot.
Put some in water and soak your feet in it. I am told it clears it up.
  Baking soda.
Use 4 teaspoons or 1 rounded Tablespoon of it per gallon of water.
Charlotte